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I'm looking for a good reference on integral equations (i.e., an equation in which an unknown function appears under an integral sign such as the Fredholm equation). I would like something accessible but covers approaches to showing existence. Any help would be much appreciated.

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    $\begingroup$ You need to tell exactly what you mean by "integral equations". Is it equations involving integers in number theory? Or the integrals we see in calculus? Or something else? $\endgroup$
    – Aryabhata
    Commented Feb 29, 2012 at 21:18
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    $\begingroup$ Search for "Smithies Integral equations" on Google books. $\endgroup$ Commented Mar 1, 2012 at 7:13

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You may think of this classic by Grippenberg, Londen, Staffans.

It is quite complete and also accessible compared to other books, but not an easy reading.

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Here is a well written book and easy to read by A. Jerri "Introduction to Integral Equations with Applications".

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Stephen M.Zemyan, The Classical Theory of Integral Equations, A Concise Treatment, Birkhauser Recently, I'm reading this book. I think it is the best one for beginner.

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I am reading Linear Integral Equations by William Vernon Lovitt and finding it quite easy to understand. If you are a beginner, you should definitely try that.

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Handbook of Integral Equations: Polyanin, Andrei D. Manzhirov is avaliable on the P2P servers or it can be found easily

it dealsh with integral equations how to solve it with examples and similar

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